Waves of autocrine signaling in patterned epithelia

C. B. Muratov, S. Y. Shvartsman

Research output: Contribution to journalArticlepeer-review

Abstract

A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is possible, using a variational approach. It is shown that under a number of assumptions which can be easily verified for particular sets of model parameters, the equation admits a unique (up to translations) variational traveling wave solution. A global bifurcation structure of these solutions is investigated in a number of particular cases. It is demonstrated that the considered setting may provide a robust developmental regulatory mechanism for delivering chemical signals across large distances in developing epithelia.

Original languageEnglish (US)
Pages (from-to)46-63
Number of pages18
JournalMathematical Modelling of Natural Phenomena
Volume5
Issue number5
DOIs
StatePublished - Jan 2010

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • cell communication
  • front propagation
  • traveling waves

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